3D Gaussian splatting (3DGS) has shown promising results in image rendering and surface reconstruction. However, its potential in volumetric reconstruction tasks, such as X-ray computed tomography, remains under-explored. This paper introduces R2-Gaussian, the first 3DGS-based framework for sparse-view tomographic reconstruction. By carefully deriving X-ray rasterization functions, we discover a previously unknown integration bias in the standard 3DGS formulation, which hampers accurate volume retrieval. To address this issue, we propose a novel rectification technique via refactoring the projection from 3D to 2D Gaussians. Our new method presents three key innovations: (1) introducing tailored Gaussian kernels, (2) extending rasterization to X-ray imaging, and (3) developing a CUDA-based differentiable voxelizer. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches by 0.93 dB in PSNR and 0.014 in SSIM. Crucially, it delivers high-quality results in 3 minutes, which is 12x faster than NeRF-based methods and on par with traditional algorithms. The superior performance and rapid convergence of our method highlight its practical value.
三维高斯绘制（3DGS）在图像渲染和表面重建中显示出有希望的结果。然而，其在体积重建任务中的潜力，例如X射线计算机断层扫描，仍然未被充分探索。本文介绍了R2-Gaussian，这是第一个基于3DGS的稀疏视图断层重建框架。通过仔细推导X射线光栅化函数，我们发现了标准3DGS公式中之前未知的积分偏差，这阻碍了准确的体积检索。为了解决这个问题，我们提出了一种通过重构从三维到二维高斯的投影的新颖矫正技术。我们的新方法呈现三个关键创新：（1）引入定制的高斯核，（2）将光栅化扩展到X射线成像，以及（3）开发基于CUDA的可微体素化器。广泛的实验表明，我们的方法在峰值信噪比（PSNR）上超过了最先进的方法0.93 dB，在结构相似性指数（SSIM）上提高了0.014。关键的是，它在3分钟内提供高质量结果，这比基于NeRF的方法快12倍，与传统算法相当。我们方法的卓越性能和快速收敛突显了其实际价值。